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Binomial Theorem
The demonstration -
Multiplication and Division of
Series . - - -
Multinomial Theorem .
Reversion of Series
Demonstration do. - -
Permutations and Combinations
Logarithms . - - -
The method of finding the increase
of Population in any country
under given circumstances of
births and mortality - 306
Figurate and Polygonal Numbers 311
Interest and Annuities . 312
Compound Interest - - 314
Wanishing Fractions and other par-
ticular expressions . 319 to 323
Decomposition of Rational Frac-
tions into their equivalent Sim-

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Indeterminate Analysis, though a
variety of forms . -
Compound Indeterminate Equa-
tions - - - 350
Continued Fractions - 368
The differential method of Series 379
Summation of the Infinite Series 382
Diophantine Analysis 390
Double and Triple Equalities 402
Solutions of a great variety of ques-
tions in this refined analysis 404,420
Miscellaneous Questions, with
their solutions and without
Some curious Questions with their
Solutions . 432–6
Deophantine Questions and Solu-
tions . 446 to 474 and 478.
Four hundred and twenty-four
Questions for Practice . 498
Further Investigation of Com-

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ple Fractions . - - 324 pound Interest and Annuity, Recurring Series . 329 twenty pages 541

[CP Table, page 572. Which shews what one dollar will amount to, being forebone or increase at Compound Interest, in any number of years not exceeding 21; and being computed yearly at any of the rates 3, 34, 4, 44, 5 and 6 per cent per annum. Table 1, page 573. Exhibiting the period in which the population of a country has a tendency to double itself, from an estimate of its increase per cent., taken at the end of every ten years. A Table of Reciprocals, squares, cubes and roots. Page 374. Page 575, top Table, which shows what $1, payable at the end of any term of years to come, under 21, is worth in ready money. Discounting or rebate being yearly computed at any of the following rates: 3, 3}, 4,4}, 5 and 6 per cent. per annum. Page 575. Table Second, at the bottom, which shows what $1 annuity, payable by yearly payments, and foreborn any number of years under 21, will amonnt to at the end of the term, Compound Interest, being computed at any of the rates to wit, 3, 3}, 4, 44, 5, and 6 per cent per annum. Page 576, the top Table. Which shews the present worth of 18, Annuity to continue any term of years under 21, and payable by yearly payments, Compound Interest being computed at any of these rates, to wit, 3,3}, 4,4}, 5 and 6 per cent. per annum. e Bottom Table on page 576, will show what Annuity payable by yearly payments to continue any term of years under 21, 18 will purchase, Compound Interest being computed at any of these rates, to wit, 3, 3}, 4, 44, 5 and 6 per cent. per annum. The Construction of Geometrical Problems, Analysis and demonstration of Theorems, page 582. Application of Algebra to Geometry, page 584. [Co. It is to be distinctly understood that I am indebted to the following works, viz. Simson's Algebra, Emerson, Bonnycastle, Euler, Saunderson, Maclaurin, Bland, Bridge, Wood, Nicholson, Newton's Universal Arithmetic, Ward, Doddridge, De Moivre's, Clairaut, Wolfius, Peacock, Muller, Hayes, Fermat, Pierse's, Diophantus, Bachet, Waring, and others, which my limits will not permit me to name.

page 577.

1. A and B purchase 900 (a) acres of land at the rate of $2 per acre, which they paid equally between them; but on dividing the same, A got that part of the farm which contained the house, and agreed to pay $#5 or $3% per acre more than B; ... 45 cts; how many acres had A and B, and at what price Let z, and a-z,

denote the number of acres A and Beach had; then #: ++o, ;

and #=#H# will be the price A and B each paid per acre,

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90000 90000 LA | M. R. Q: gy H5 or ā- $y +40; or go–H3100,–1800000, and y=500, as before. 2. A man buys 80 pounds of pepper and 36 pounds of saffron, so that for $8, he had 14 pounds of pepper more than he had of saffron for $26, and what he laid out amounted to $188. How many pounds of pepper had he for $8, and how many of saffron for $26. Ans. 20 pounds of pepper and 6 of saffron. Let a denote number of pounds of pepper that he bought for $8, and y = number of pounds of saffron for $26, then by the question if a pounds cost $8 what will 80 pounds cost, and if y pounds of saffron cost 26 dollars what will 36 pounds of saffron

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